Questions on Algebra: Quadratic Equation answered by real tutors!

Tutors Answer Your Questions about Quadratic Equations (FREE)

Question 1075688: Please help me solve this problem : Find the value of the constant k such that the ratio of the two
solution of the quadratic equation 2x2 + kx + k +2 = 0 is 3:2
Click here to see answer by ikleyn(52748)

Question 1075729: For what real values of a does the quadratic 4x^2 + ax + 25 have non-real roots? Give your answer as an interval.

Click here to see answer by josmiceli(19441)

Question 1075731: The solutions to the equation (x+1)(x+2) = x+3 can be written in the form m+sqrt(n) and m-sqrt(n), where m and n are integers. What is m+n?
Click here to see answer by josgarithmetic(39613)

Question 1075730: Find one pair of real numbers, (x,y), such that x + y = 6 and x^3 + y^3 = 144.

Click here to see answer by ikleyn(52748)

Question 1075801: Solve 4x2 − 80 = 0. Choose the correct answer rounded to three decimal places.
Click here to see answer by jorel1380(3719)

Question 1075906: Write a trinomial that represents the area of the trapezoid.
Base 1: 2x+1
Base 2: 3x+3
Height: x+3
Click here to see answer by MathLover1(20849)

Question 1075920: Consider a circle whose radius is greater than 9 and area is given by A=x^2-17x+66. Use factoring to find an expression for the radius of the circle.
Click here to see answer by Alan3354(69443)

Question 1076058: how many solutions does x^2+4x=-3
Click here to see answer by josgarithmetic(39613)

Question 1076100: Please help me solve this by COMPLETING THE SQUARE
28x-2x^2=26
I got no real solution. This is what I did, please correct me.
-2x^2+28x=26
(28/2)^2=196
-2x^2+28x+196=26+196
since you cannot take the square root of a negative, i got no real solution

√-2x^2 = no real solutions
Please help me, I am very confused. Thank you in advance, Emily
Click here to see answer by Alan3354(69443)

Question 1076113: Harrison solved the equation below. Is his solution correct? Explain why or why not.
x^2-6x-7=0
x^2-6x=7
x^2-6x+9=7+9
(x-3)^2=16
x-3=16
x=19
x-3=-16
x=-13
Click here to see answer by MathLover1(20849)

Question 1076111: 1. (a) Explain why the equation (𝑥−4)^2−28=8 has two solutions.
(b) Solve the equation to find the solutions. Show your work.

Click here to see answer by josgarithmetic(39613)

Question 1076226: How would you simplify
y= 2(x+3)^2 - 8
&
how would you factor
y= x^2 + 3x - 18
Click here to see answer by MathLover1(20849)

Question 1076226: How would you simplify
y= 2(x+3)^2 - 8
&
how would you factor
y= x^2 + 3x - 18
Click here to see answer by Alan3354(69443)

Question 1076226: How would you simplify
y= 2(x+3)^2 - 8
&
how would you factor
y= x^2 + 3x - 18
Click here to see answer by jorel1380(3719)

Question 1076233: The length of the base of a triangle is twice its height. If the area of the triangle is 25 square kilometers, find the height.
Click here to see answer by jorel1380(3719)

Question 1076232: The product of two consecutive room numbers is 156. Find the room numbers.
Click here to see answer by jorel1380(3719)

Question 1076231: Find the length of the shorter leg of a right triangle if the longer leg is 14 feet more than the shorter leg and the hypotenuse is 14 feet less than twice the shorter leg.
Click here to see answer by jorel1380(3719)

Question 1076241: solve for x. x^2+6677x+22
Click here to see answer by Alan3354(69443)

Question 1076230: The length of a rectangle is 29 centimeters less than six times its width. Its area is 42 square centimeters. Find the dimensions of the rectangle.
Click here to see answer by jorel1380(3719)

Question 1076346: Solve by completing the square. The equation is 25x^2+30-12=0
Click here to see answer by MathLover1(20849)

Question 1076346: Solve by completing the square. The equation is 25x^2+30-12=0
Click here to see answer by MathTherapy(10549)

Question 1076357: If the sides of a square are shortened by 4 cm, the area becomes 36 cm. find the length of a side of the original square.
Click here to see answer by Boreal(15235)

Question 1076357: If the sides of a square are shortened by 4 cm, the area becomes 36 cm. find the length of a side of the original square.
Click here to see answer by josmiceli(19441)

Question 1076462: A monic quadratic is a quadratic in which the coefficient of the quadratic term is 1. For example, r^2 - 3r + 7 is a monic quadratic, but 3t^2 - 3t + 1 is not.
A teacher writes a monic quadratic on the board.
Joanie copies the quadratic onto her paper, but writes down the wrong constant term (but the correct quadratic and linear terms). She correctly factors the quadratic that she wrote down on her paper, and determines that her quadratic has roots -16 and 2.
Kelvin is factoring the same quadratic that the teacher wrote on the board. He also copies the quadratic onto his paper, but he writes down the wrong coefficient for the linear term (but the correct quadratic and constant terms). He correctly factors the quadratic that he wrote down, and determines that his quadratic has roots -36 and 2.
What are the roots of the quadratic that the teacher wrote on the board?
Click here to see answer by KMST(5328)

Question 1076439: use the information provided to write the equation of each parabola
focus(-12,0) directrix x=12
please show work
Click here to see answer by josgarithmetic(39613)

Question 1076537: What are the solutions to the system of equations?
x^2+y^2=5
y=2x
(___,2)and(___,___)
Click here to see answer by ikleyn(52748)

Question 1076649: How many solutions exist for the system below?
In two or more complete sentences, give the solution and explain how you solved the system.
y=-2x+3
y=-2x*3^x
Graph: https://vallejocity.owschools.com/media/g_alg01_ccss_2016/9/img_alg1u09l03_02.gif
Click here to see answer by Theo(13342)

Question 1076722: Use technology to approximate the solution(s) to the system of equations to the nearest tenth of a unit.
Equation: https://vallejocity.owschools.com/media/g_alg01_ccss_2016/9/l19a_q7.gif
Click here to see answer by ikleyn(52748)

Question 1076720: Use technology to approximate the solution(s) to the system of equations to the nearest tenth of a unit.
equation:
https://vallejocity.owschools.com/media/g_alg01_ccss_2016/9/l19a_q6.gif
Click here to see answer by ikleyn(52748)

Question 1076736: If both the roots of the equation
lie between -3 and 5 then k lies between
Click here to see answer by josgarithmetic(39613)

Question 1076750: write the equation of a parabola that opens upward with an axis of symmetry of x=-7/2
Click here to see answer by alanc(27)

Question 1076897: x2-6x+2=0 it wants you to solve using quadratic formula

Click here to see answer by stanbon(75887)

Question 1076898: hi please i need your help with this problem
an object is projected vertically upward from the ground at an initial velocity of 192 feet per second if air resistance is neglected, its distance s(t) is given by s(t)=-162t^2+192
a-find the maximum height the object reaches and the number of seconds it takes to reach that height. write the answer using a complete sentence
b- when will the object hit the ground
thank you
Click here to see answer by jorel1380(3719)

Question 1076983: Hello can someone help me with this please,
One of the earliest known quadratic equations come from a 3800-year-old document from acient Egypt that now sits in the Berlin museum in Germany . Translated into Modern mathematical notation the document now known as the Berlin Papryus poses the following set of equations
x^2+y^2=100 Y=3/4x
Solve for the values of x and y
Click here to see answer by rapture(86)

Question 1077053: Larry's time to travel 255 miles is one hour more than Terrell's time to travel 220 miles. Terrell drove four miles per hour faster than Larry. how fast did each one travel?
Click here to see answer by ikleyn(52748)

Question 1077131: A model rocket is launched with an initial velocity of 164 ft/sec. Its height h, in feet, after t seconds is given by the formula h =16t^2-164t. After how many seconds will the rocket first reach a height of 348 ft?

Click here to see answer by jorel1380(3719)

Question 1077181: How do I find width for a quadratic equation word problem?
I have Area=160, Leangth=w+12, and I can't find Width.
help!
Click here to see answer by MathLover1(20849)

Question 1077256: The vertex of this parabola is at (-4, -1). When the y-value is 0, the x-value is 2. What is the coefficient of the squared term in the parabola's equation?

Click here to see answer by josgarithmetic(39613)

Question 1077217: A positive real number is 1 more than another. When -2 times the smaller is added to the square of the larger the result is 46. Find the numbers. If applicable right in form p+q square root of r
Click here to see answer by josgarithmetic(39613)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 17551..17595, 17596..17640, 17641..17685, 17686..17730, 17731..17775, 17776..17820, 17821..17865, 17866..17910, 17911..17955, 17956..18000, 18001..18045, 18046..18090, 18091..18135, 18136..18180, 18181..18225, 18226..18270, 18271..18315, 18316..18360, 18361..18405, 18406..18450, 18451..18495, 18496..18540, 18541..18585, 18586..18630, 18631..18675, 18676..18720, 18721..18765, 18766..18810, 18811..18855, 18856..18900, 18901..18945, 18946..18990, 18991..19035, 19036..19080, 19081..19125, 19126..19170, 19171..19215, 19216..19260, 19261..19305, 19306..19350, 19351..19395, 19396..19440, 19441..19485, 19486..19530, 19531..19575, 19576..19620, 19621..19665, 19666..19710, 19711..19755, 19756..19800, 19801..19845, 19846..19890, 19891..19935, 19936..19980, 19981..20025, 20026..20070, 20071..20115, 20116..20160, 20161..20205, 20206..20250, 20251..20295, 20296..20340, 20341..20385, 20386..20430, 20431..20475, 20476..20520, 20521..20565, 20566..20610, 20611..20655, 20656..20700, 20701..20745, 20746..20790, 20791..20835, 20836..20880, 20881..20925, 20926..20970, 20971..21015, 21016..21060, 21061..21105, 21106..21150, 21151..21195, 21196..21240, 21241..21285, 21286..21330, 21331..21375, 21376..21420, 21421..21465, 21466..21510, 21511..21555, 21556..21600, 21601..21645, 21646..21690, 21691..21735, 21736..21780, 21781..21825, 21826..21870, 21871..21915, 21916..21960, 21961..22005, 22006..22050, 22051..22095, 22096..22140, 22141..22185, 22186..22230, 22231..22275, 22276..22320, 22321..22365, 22366..22410, 22411..22455, 22456..22500, 22501..22545, 22546..22590, 22591..22635, 22636..22680, 22681..22725, 22726..22770, 22771..22815, 22816..22860, 22861..22905, 22906..22950, 22951..22995, 22996..23040, 23041..23085, 23086..23130, 23131..23175, 23176..23220, 23221..23265, 23266..23310, 23311..23355, 23356..23400, 23401..23445, 23446..23490, 23491..23535, 23536..23580, 23581..23625, 23626..23670, 23671..23715, 23716..23760, 23761..23805, 23806..23850, 23851..23895, 23896..23940, 23941..23985, 23986..24030, 24031..24075, 24076..24120, 24121..24165, 24166..24210, 24211..24255, 24256..24300, 24301..24345, 24346..24390, 24391..24435, 24436..24480, 24481..24525, 24526..24570, 24571..24615, 24616..24660, 24661..24705, 24706..24750, 24751..24795, 24796..24840, 24841..24885, 24886..24930, 24931..24975, 24976..25020, 25021..25065, 25066..25110, 25111..25155, 25156..25200, 25201..25245, 25246..25290, 25291..25335, 25336..25380, 25381..25425, 25426..25470, 25471..25515, 25516..25560, 25561..25605, 25606..25650, 25651..25695, 25696..25740, 25741..25785, 25786..25830, 25831..25875, 25876..25920, 25921..25965, 25966..26010, 26011..26055, 26056..26100, 26101..26145, 26146..26190, 26191..26235, 26236..26280, 26281..26325, 26326..26370, 26371..26415, 26416..26460, 26461..26505, 26506..26550, 26551..26595, 26596..26640, 26641..26685, 26686..26730, 26731..26775, 26776..26820, 26821..26865, 26866..26910, 26911..26955, 26956..27000, 27001..27045, 27046..27090, 27091..27135, 27136..27180, 27181..27225, 27226..27270, 27271..27315, 27316..27360, 27361..27405, 27406..27450, 27451..27495, 27496..27540, 27541..27585, 27586..27630, 27631..27675, 27676..27720, 27721..27765, 27766..27810, 27811..27855, 27856..27900, 27901..27945, 27946..27990, 27991..28035, 28036..28080, 28081..28125, 28126..28170, 28171..28215, 28216..28260, 28261..28305, 28306..28350, 28351..28395, 28396..28440, 28441..28485, 28486..28530, 28531..28575, 28576..28620, 28621..28665, 28666..28710, 28711..28755, 28756..28800, 28801..28845, 28846..28890, 28891..28935, 28936..28980, 28981..29025, 29026..29070, 29071..29115, 29116..29160, 29161..29205, 29206..29250, 29251..29295, 29296..29340, 29341..29385, 29386..29430, 29431..29475, 29476..29520, 29521..29565, 29566..29610, 29611..29655, 29656..29700, 29701..29745, 29746..29790, 29791..29835, 29836..29880, 29881..29925, 29926..29970, 29971..30015, 30016..30060, 30061..30105, 30106..30150, 30151..30195, 30196..30240